Chain Rule and Trig

1. Block 2
Elur Niahc and Trig

2. What is to be learned?
• How to integrate trig functions
• How to apply Elur Niahc to trig functions

3. Chain Rule
y = sin(3x + 10)
let y = sin U , where U = 3x + 10
dy
/du
du
/dx
= Cos U 3dy
/dx
= cos U = 3
= 3Cos(3x + 10)
÷ 3

4. ∫
= Sin (ax + b)
a
∫ Cos (ax + b)
∫ Cos (2x + 7)
dx
dx
= Sin(2x + 7)
2
+ c
+ c

5. Chain Rule
y = cos(3x + 10)
dy
/dx = -3sin(3x + 10)
÷ -3

6. ∫
= -Cos (ax + b)
a
∫ Sin (ax + b)
∫ Sin 4x
dx
dx
= -Cos 4x
4
+ c
+ c

7. ∫
= Sin (4x – 3)
4
∫ Cos (4x – 3) dx
+ c
∫ 3Sin(5x + 1) dx
= -3Cos (5x + 1)
5
+ c

8. Elur Niahc and Trig
∫
= -Cos (ax + b)
a
∫Sin (ax + b) dx
∫
= Sin (ax + b)
a
∫ Cos (ax + b) dx
+ c + c
Version is on formula sheet

9. ∫
= 9Sin (6x – 2)
6
∫ 9Cos (6x – 2) dx
+ c
2
3
= 3Sin (6x – 2)
2
+ c

10. ∫ 6Sin(8x + 1) dx
= -6Cos (8x + 1)
8
+ c
= -3Cos (8x + 1)
4
+ c
Key Question

11. 6
-6
y = 6sin2x
Shaded area = ∫
1800ππ
/2
0
π
/2
6sin2x dx
= -6cos 2x
2
[ ]
0
π
/2
= -3cos π – -3cos 0
= -3(-1) – -3(1)
= 6 units2